I have a doubt how to notate this particular problem.
I have several lines/instruments in the score, and independent accelerando.

The first line A starts playing at T=48. The phrase is not according to the time signature neither the beats, so the initial "simple" rhythm becomes more complex across the barlines and across the beats.
[Here I have idea to write it down exactly, but above the top note of the each phrase I would write the number of repetition: (2) (3) (4) ... ]

The second line B starts at the tempo change 5:4, so now is T=60ca. The similar problem, as above, is here apparent too.
But, there is another issue. The first line A must keep playing at the initial T=48 regardless of the conductor.
[Now, here I can write down the line A as it would be in the new tempo, perhaps with the reduced size. It will be a lot of tuplets etc, but I could write above also the numbering of the each phrase, so the musician would just count, and the notation is just for orientation.

The next tempo change is the same 5:4, so the next tempo is T=75ca, after that T=94ca and finally T=117ca. Here all problems are multiplied, but the principle is the same.

The idea to have numbered repetitions is quite clear, but the notation can be written differently.

The first option, as mentioned above, is to write it down exactly as it has to be performed in the new tempo, with reduced size, and this will be used just as an orientation (w. repetition number above).

The second option is to notate the phrase exactly as it is the first time, ignoring the beaming, bar-lines etc. The fact is that the first played phrases are going to be larger and larger (longer and longer, across measures), as the tempo increases. (also w. repetition number)

The third option is to write a long line across the measures with the text "keep repeating independently in the initial tempo" and using vertical arrows (w. repetition number) to sign the start points of the each phrase, but since the measure is completely empty I should use vertical ticks as the beat symbols, or similar.

I hope the description is clear for your visualisation. I think I am going to use Finale for this project.

I'd love to help, OCTO., but the situation is not clear to me. Some sort of example might be helpful. You mentioned repetition numbers. Are these lines A, B etc. each made up of short phrases repeated many times? The kind that would be enclosed in repeat marks followed by a long thick line to show the extent of the repetition? And do these lines A, B, enter, one after the other each time alla fuga but at a new tempo while each continues repeating the same phrases?

Gould has a section called Freedom and Choice at the end of her book. Perhaps that would help?

Are the lines played by single players or by multiple players at the same time? In the latter case: will the players be close to each other or on different sides of the orchestra? Is the rhythmic structure so complicated that the players that play the same line need the conductor to play together, even when he is already conducting the next tempo? Or, looking at the whole thing: is it important that the different lines are performed precisely in rhythmic relation with each other? For me these would be the only reasons to choose your first option. Otherwise you'd produce something absurdly complicated that doesn't actually help.

If utmost precision is not what you're aiming for I would probably vote for option three.

Just my two cents, based on my understanding of your description. Which might be completely off track of course…

I also would like to help, but I cannot get a clear enough picture of what you're trying to notate. Maybe a little hand-written sketch would help us?
What is "the phrase" like? Just short repeated motive? What rhythm is "the initial simple rhythm"?
If the phrase "is not according to the time signature [nor] the beats", what does it mean when you say the phrase is in T=48?
You say "independent accelerando", but then you say "keep repeating in the initial tempo". So accelerando or no accelerando?
Which tempo is the conductor's tempo?
Is the number of repetitions in each part predetermined or open?
(Plus the other questions already asked by others.)